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Answer:

Step-by-step explanation:
The interval of interest becomes the limits of integration. ∆x becomes dx, and the xi are replaced by the variable of integration, x.
Answer:
The value of a function is the actual calculation done at a certain point. The limit is - roughly speaking - the value at points that are “arbitrarily close” to the same point. For most commonly used functions, the value of a function at a point, and the limit at the same point, is the same - at least for most values.